Pricing Generalized Dispersion Swap for Multi-Asset Stochastic Volatility Models

Abstract

This paper develops a generalized variance framework for pricing multi-asset dispersion swap based on the determinant of the instantaneous covariance matrix of asset log-returns. This determinant-based measure captures the joint dispersion of multivariate asset returns while accounting for their dependence structure. We formulate the proposed framework under the Heston and Barndorff-Nielsen-Shephard (BNS) stochastic volatility models, deriving an analytical pricing expression for the three-asset Heston formulation and a tractable approximation for the corresponding BNS formulation. To assess the empirical performance of the proposed approach, we conduct numerical experiments using nine stocks obtained through the quantmod package, randomly partitioned into three groups of three assets. The models are calibrated and evaluated against empirical generalized realized variance across selected time horizons.